Spectral functions in the $\phi^4$-theory from the spectral DSE

TL;DR

This paper introduces a non-perturbative spectral framework for calculating real-time correlation functions in strongly correlated systems, ensuring symmetry preservation and applying it to compute spectral functions in 2+1 dimensional $\

Contribution

It develops a spectral renormalisation approach compatible with various functional methods and applies it to compute spectral functions in $\

Findings

Computed non-perturbative spectral function of scalar field in 2+1 $\

Analyzed the $s$-channel spectral function of the $\

Demonstrated symmetry-preserving spectral renormalisation in functional approaches.

Abstract

We develop a non-perturbative functional framework for computing real-time correlation functions in strongly correlated systems. The framework is based on the spectral representation of correlation functions and dimensional regularisation. Therefore, the non-perturbative spectral renormalisation setup here respects all symmetries of the theories at hand. In particular this includes space-time symmetries as well as internal symmetries such as chiral symmetry, and gauge symmetries. Spectral renormalisation can be applied within general functional approaches such as the functional renormalisation group, Dyson-Schwinger equations, and two- or $n$-particle irreducible approaches. As an application we compute the full, non-perturbative, spectral function of the scalar field in the $\phi^4$-theory in $2+1$ dimensions from spectral Dyson-Schwinger equations. We also compute the $s$-channel spectral function of the full $\phi^4$-vertex in this theory.